# Math Help - finding the rate of change of height of cone.

1. ## finding the rate of change of height of cone.

maths prob.bmp

Hi guys, i am having problem to solve the above question, i seem not able to get the correct answer each time i try out.

Hope someone could help me out. Thanks.

2. ## Re: finding the rate of change of height of cone.

Think of the volume $V$ of water in the conical container as being composed of circular disks of thickness $dh$. We may then state:

$\frac{dV}{dt}=\pi r^2\frac{dh}{dt}$

We know the ratio of the radius of the water's surface to the height of the water level will be the same as that of the container:

$r=\frac{2}{3}h$ hence:

$\frac{dV}{dt}=\pi \left(\frac{2}{3}h \right)^2\frac{dh}{dt}$

Now, solve for $\frac{dh}{dt}$ and use the given values of $\frac{dV}{dt},h$ to compute the requested value.